Tips on Technicals - Log Scales
In many areas of technical analysis, it is necessary to compare two bits of unlike data (apples and oranges, if you will). These can be the prices of stocks versus bonds or a single item's price versus its momentum. When analyzing an item or market over the long term, it is common to compare trends and price patterns at different price levels. If prices have not moved much in relation to their absolute price level, ordinary arithmetic scaling is sufficient. For example, Eurodollar futures have traded in a seven point range centered around a price of 93 for the past decade. In percentage terms, 7 / 93 = ~ 7.5%.
When prices move in large percentages, trendline construction can be subjective and analysis unreliable. Logarithmic (Log) scaling overcomes this problem. Rather than simply plotting price on the vertical axis in a linear fashion, prices are plotted to indicate percentage changes. This means that the vertical distance drawn for an item that doubles in price is the same whether it goes from 5 to 10 or from 100 to 200. A linear scale would plot the same vertical distance from 5 to 10 as it would for 100 to 105.
In Figure 1, the charts show the stock price for MicroSoft since mid-1986. Notice the price scales of the two charts are very different. Both start near 1 1/2 in 1986 and end near 54 in 1994. However, when prices rose from 2 to 4 in 1987, the linear scale on the left shows a very small move. The log scale on the right shows a very large move.
Figure 1
The vertical distance on the log scale for the move from 2 to 4 is the same as that of the move from 20 to 40. This simply means that prices doubled and provides for valid comparisons at any price level. It also allows for better trendline and pattern analysis. Note that the congestion zone taking place in 1988 and 1989 shows up much more clearly as a triangle pattern on the log scale. Note also that what appears to be a period of high volatility in 1992 and 1993 on the linear scale is put into better perspective on the log scale. Prices were no more volatile there than they were throughout the entire 9 year period shown.
Finding the Trend
Figure 2 shows 5 years of weekly data for the Hang Seng Stock Index in Hong Kong. The chart on the left has a linear scale and the chart on the right has a log scale. When a trendline is drawn on the linear chart from the start of the long rally, prices traded higher away from the trend. This acceleration of the rally would incorrectly indicate that the market was moving too far, too fast and that a correction would occur soon. In early 1992, after being "overbought" for more than a year, prices accelerated their rise even more. In 1993, prices again appeared "overbought" when compared to the new, steeper trendline, and still continued to rise. Any trader reacting to this ever increasing rate of price movement by selling would have sustained significant losses.
Figure 2
If the trader had used the log scaled chart on the right, he would have been able to see that the long term trend in prices was consistent and this would have allowed him to do better analysis on the market. While the very strong decline in 1994 looked like it was accompanied by extreme volatility, it was actually less disastrous than the decline of early 1990 when the market lost an even higher percentage of its value. A linear chart simply does not show this condition.
Conclusion
Logarithmic scaling is sometimes called ratio scaling and perhaps that is a better name. It tries to measure changes in value, rather than absolute prices. For example, a portfolio of 2 million ECU is equally invested in one security purchased at 10 and another purchased at 100. Both markets rise 90 points so the first security is worth 100 and the second is worth 190. However, the first has gone up 10 times in value to 10 million and the second only 0.9 times to 1.9 million. In other words, significantly more profits were generated with the first security and the charts should reflect that fact. Log scaling allows the trader to see a clearer picture of percentage changes than arithmetic scaling when markets move to different price levels.
